Modulation format identification (MFI) is a key technology in optical performance monitoring for the next-generation optical network, such as the intelligent cognitive optical network. An MFI scheme based on the Calinski–Harabasz index for a polarization-division multiplexing (PDM) optical fiber communication system is proposed. The numerical simulations were carried out on a 28 Gbaud PDM communication system. The results show that the required minimum optical signal-to-noise ratio values of each modulation format to achieve 100% identification accuracy are all equal to or lower than their corresponding 7% forward error correction thresholds, and the proposed scheme is robust to residual chromatic dispersion. Meanwhile, the proposed scheme was further verified by 20 Gbaud PDM-QPSK/16QAM/32QAM long-haul fiber transmission experiments. The results show that the scheme has a good reliability when fiber non-linear impairments exist. In addition, the complexity of the scheme is significantly lower than that of other clustering-based MFI schemes.

Nonlinear frequency division multiplexing (NFDM) has been shown to be promising in overcoming the fiber Kerr nonlinearity limit. In multiple-eigenvalue modulated NFDM systems, the transmission capacity increases with the number of modulated eigenvalues. However, as the number of modulated eigenvalues increases, the complexities of the signal waveform and the nonlinear Fourier transform (NFT) algorithm for demodulation increase dramatically as well, while the accuracy drops significantly. Meanwhile, impairments such as amplifier spontaneous emission noise and phase noise in practical channels would perturb the eigenvalues and the corresponding nonlinear spectra during transmission. Coupled with an increase in the modulation format order, it is difficult for NFT algorithm-based receivers to recover information. To enable the use of multiple-eigenvalue modulated NFDM systems, we propose an innovative receiver based on regression neural networks (NNs), which can demodulate information correctly for both single- and dual-polarization NFDM systems. The results show that it has strong robustness and has a certain tolerance to the impairments of communication systems. In the contrast that the poor demodulation performance of the NFT and the Euclidean minimum distance (MD) receivers for multi-eigenvalue modulated NFDM systems, our proposed NN receiver can achieve low bit error rate with 2 GBaud 16QAM modulation over 1,000 km transmission in four-eigenvalue modulated single-polarization NFDM systems. The performance of three receivers (NFT, MD and NN) in a two-eigenvalue modulated NFDM system are also compared, the NN receiver shows the best performance and appears more suitable for higher-order modulation formats.

A joint scheme introducing probabilistic shaping (PS) at the transmitter and utilizing a neural network (NN) equalizer at the receiver is proposed to improve the performance of the b -modulated nonlinear frequency division multiplexing (NFDM) system. Through a numerical simulation, we demonstrate that PS plays a leading role for low launch power case, which improves the performance of the system effectively, while the NN equalizer’s superiority appears in a high launch power region, whose main role is to weaken the correlation among subcarriers for improving system performance. The proposed scheme would enlighten the optimum modulation and detection schemes of the NFDM system.

A lightweight two-stage convolutional (deep) neural network (CNN) based modulation format identification (MFI) scheme is proposed and demonstrated for the polarization domain multiplexing (PDM) fiber communication system with probabilistically shaped (PS) modulation formats. The scheme is tested on a PDM system at a symbol rate of 28 GBaud. Six probabilistically shaped (PS) modulation formats (of 3 bit/symbol PS-16QAM, PS-32QAM, and PS-64QAM, of 4 bit/symbol PS-32QAM and PS-64QAM, and of 5 bit/symbol PS-64QAM) along with six standard modulation formats (BPSK, QPSK, 8PSK and three uniformly shaped (US) QAM: US-16QAM, US-32QAM and US-64QAM) are identified by the trained CNN. By taking advantage of computer vision, the results show that the proposed scheme can provide very high accuracy and significantly improve the identification performance over the existing techniques. The influences of the learning rate of the CNN are also discussed.

We investigated beam shifts for an arbitrarily polarized vortex beam reflected and transmitted at two-dimensional (2D) anisotropic monolayer graphene surface. And generalized expressions are theoretically derived for calculating beam shifts of vortex beam. Then, we presented the beam shifts associated with the self-isotropic (SI) effect, self-anisotropic (SA) effect and cross-coupling (XC) effect originated from self-isotropic interaction, self-anisotropic interaction and cross-coupling interaction between isotropic and anisotropic of two-dimensional media, respectively. More importantly, novel optical phenomena resulting from the XC effect are flexibly shown by manipulation OAM. We believe that our results can be extensively extended to 2D anisotropic Dirac semimetals and Weyl semimetals, and expect the results to be significant and contribute to the understanding of the spin and orbit Hall effect of the light.